Solve for $d$. Give an exact answer. $0.5(7d+4)=7-1.5d$ $d =$
Solution: We need to manipulate the equation to get $ d $ by itself. $\begin{aligned} 0.5(7d+4) &= 7-1.5d \\\\ 3.5d+2 &= 7-1.5d~~~~~~~~~~\gray{\text{Distribute}}\\\\ 3.5d+2{+1.5d} &= 7-1.5d{+1.5d} ~~~~~~~~~~\gray{\text{Add 1.5d to each side}}\\\\ 5d+2&=7 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 5d+2{-2} &= 7{-2} ~~~~~~~~~~\gray{\text{Subtract 2 from each side}}\\\\ 5d&=5 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{5d}{{5}}&= \dfrac{5}{{5}}~~~~~~~~~~\gray{\text{Divide each side by 5}} \\\\ d &= {1} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $d = { 1 }~~~~~~~~$ [Let's check our work!]